Limit laws for empirical optimal solutions in random linear programs

Abstract We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding program, we characterize under assumptions fluctuations of empirical optimal solutions around their population quantities after standardization by distributional limit theorem. Our approach geometric nature and further relies on duality collection dual feasible basic solutions. The limiting variables are driven amount degeneracy inherent programming. In particular, if degenerate asymptotic law might not be unique determined from way solution chosen. Furthermore, include consistency convergence rates Hausdorff distance between true optimality sets as well for value involving set all analysis motivated statistical transport that particular interest here laws plans follow simple application our theory. distribution usually non-Gaussian which stands strong contrast recent finding entropy regularized